AP/Calculus-Based Physics:Wave Energy Units

Examples of all types of waves are found in nature. Our understanding of the physical world is not complete until we understand the properties and behaviors of waves. Mechanical waves require a material "medium" through which to travel, electromagnetic waves do not.

Lesson Plans:

This is a unique, standards-based unit of instruction on Waves created by a high school teacher to be used with PhET interactive simulations on wave motion. It includes comprehensive lesson plans, lecture presentations, and assessments with answer keys. Be sure not to miss the "Clicker Questions" -- great introductory material.

This PhET Gold Star-winning resource is a set of 60+ Power Point concept questions on the topic of waves, available for free download. They were created by a high school physics teacher to be used with three PhET simulations: Wave on a String, Fourier Analysis, and Sound. Concept questions are designed to introduce a topic and probe student understanding BEFORE formal instruction. This method has been correlated with improved learner outcomes in studies conducted by physics education researchers.

Cross-disciplinary resource blends physics, earth science, and global history to get students excited about the science of tsunamis. It is a highly engaging way to introduce your students to the basic wave properties of frequency, amplitude, and periodicity. They use real-time data to see how various global agencies monitor for tsunami activity, then develop a "preparedness plan" using evidence from the data they collected. Most appropriate for grades 8-12, but could be adapted for Grades 6-7.

Activities:

From research in physics education, there is increasing awareness that students come into a physics class with firmly held beliefs that cannot be ignored. These use hands-on activities and probing questions to draw out misconceptions and facilitate learning. They are designed for cooperative learning groups, with complete sets of student activities and problems. Accompanying solutions are to be distributed to groups before they leave class, thus giving immediate feedback.

A collection of problems developed to engage students in metacognition, or "thinking about how they think". These are context-rich problems that attempt to link a student's qualitative understanding of concepts with real-life scenarios. Topics include masses on springs, pendulums, sound, and waves on a string. **Appropriate for students in AP or Section B calculus-based high school physics.

If you have not yet used video analysis software with your students, be prepared for a paradigm shift in your teaching! This resource provides free software called "Tracker", developed to help students closely analyze the motion of objects in a short video clip. It also allows them to create dynamical models that overlay the video to see how well the model matches the real world. Detailed instructions are provided. And it's free.

This collection is a cost-free online textbook integrating the topics of waves, sound, music, and musical instruments. Designed for use in the high school classroom, it also provides content support for teachers 6-12.

A must-read article from Science magazine, this item summarizes the research efforts of the PhET project on the use of interactive simulations in the physics classroom. Results indicate that concept mastery is measurably improved when students explore simulated physical processes in addition to traditional labs. Use of simulations was also correlated to higher student motivation and active involvement in the learning process.

This Power Point presentation condenses the results of a study on student misconceptions about wave mechanics and motion. The results indicate that many students have incorrect mental models of waves and use these erroneous models to interpret/solve problems. The researchers also tested teaching methods to see what may help students overcome these difficulties. A must-read for the teacher of advanced students who will study calculus-based physics in college.

Content Support For Teachers:

A straightforward tutorial suitable for crossover teachers or K-8 physical science teachers who would like a refresher on the topic of waves. This is part of the respected Physics Classroom tutorial collection, and covers wave categories, properties and behavior of waves, and how waves transport energy.

New and crossover teachers often appreciate a way to "see" physics beyond the pages of a textbook. This interactive tutorial covers every topic typically studied in an introduction to Waves. There are 20 sequenced tutorials, each with a discussion of one focused idea, a Java simulation that depicts that idea, and self-guided questions at the end.

Don't be scared off by the title of this item. It's a fascinating resource that features a "thematic search engine" for locating information and examples of sound, sound waves, acoustics, hearing, and other related topics. Each topic is accompanied by audio clips from the library of the World Soundscape Project. For example, the topic "Hearing Loss" contains an audio simulation of normal and impaired hearing as a result of noise exposure. Students will enjoy playing around with this one.

Student Tutorials:

Many students benefit from a simulation-based exploration of physics phenomena that allows them to self-pace. This is a set of 20 sequenced tutorials on the topic of Waves, developed to promote understanding of processes that can't be visualized in a textbook illustration. Each tutorial has a discussion section, a Java simulation the students can manipulate, and self-guided questions at the end.

Assessment:

Peer Instruction, a well-researched teaching method developed by Harvard professor Eric Mazur, is intended to actively engage students while also allowing the teacher to gauge understanding of a single concept. Students individually "vote" on a correct response to a carefully-constructed problem, then discuss their reasoning with peers. This is a set of annotated Peer Instruction problems on the topic of waves.

Lesson Plans:

A great way to spark student interest in wave motion is through the study of tsunamis. This magazine article, which appeared in The Physics Teacher in 2006, provides a step-by-step blueprint for constructing your own low-cost tsunami tank for experimenting in the classroom. Related classroom activities capture the essential physics of tsunamis. Try teaming these activities with the interactive computer simulation below, "Michigan State Tsunami Simulator".

Activities:

This simple, yet highly visual experiment uses dynamics trolleys, springs, and spring holders to model a transverse and a longitudinal wave. The models are easy enough for students to set up, but allow exploration of complex concepts, such as how this dispersive system differs from a continuous wave medium like a rope or slinky (see experiment below for a companion activity).

A Slinky spring is one of the best ways to model both transverse and longitudinal waves. Teaching tips in this web site explain how to get the best results. Try teaming this experiment with the one above that uses dynamics trolleys connected by springs. Students can compare/contrast the wave motion in a continuous versus a dispersive system (trolleys).

A set of 3 high-quality video clips that show wave pulses on a Slinky spring. One depicts a transverse wave pulse and its reflection off an fixed end. A second shows a longitudinal pulse, and the third shows two wave pulses passing over each other. For free software tools to do computer analysis of these videos frame-by-frame, see the "Tracker Video Analysis" item below.

This simple simulation is the best we have found to model the destructive energy of a tsunami for beginning students. It shows very clearly how a tsunami (which may appear insignificant at the point of origination) gains amplitude as it approaches shore, thus becoming one of nature's most destructive forces. Change the shape of the sea bottom near the coast and watch the effect on the approaching tsunami. See the instructor's guide in "Lesson Plans" (above) for directions on building a low-cost tsunami tank for classroom experiments.

This is a free video software tool for analyzing the motion captured in short video clips. Its features include position, velocity, and acceleration tracking, multiple reference frames, and model analysis. Students can analyze the motion of objects in a video and overlay simple dynamical models on the video to see how well the model matches the real world. A detailed "help" section is available to users who are newcomers to video analysis software.

References and Collections:

A great resource to augment a module on tsunamis. These are interactive "magazine-style" articles designed to help students understand how tsunamis are generated and why they become so destructive upon reaching shore. Don't miss the excellent animated view of a tsunami caused by subduction zone earthquake.

One way to get students excited about wave energy is to study tsunamis. How can a wave that is barely visible to a ship at sea become so destructive upon reaching a shoreline? This set of tutorials, simple enough for students to understand, explains how these catastrophic wave trains originate and propagate through vast oceanic distances. Each tutorial is accompanied by simulations that model the fundamentals of this phenomenon.

Student Tutorials:

This page, part of an award-winning web site on wave animations, depicts how particles move in four types of waves: longitudinal, transverse, water, and Rayleigh surface waves. Students can clearly see that the particles do not move along with the waves, they simply oscillate back and forth as the wave passes by.

Lesson Plans:

This exemplary unit of instruction was developed by a high school physics teacher to be used with PhET simulations. It includes six complete lesson plans that explore wave properties, the physics of sound, Fourier analysis, and wave phenomena such as reflection and superposition. Most of the lessons require that the simulation be open on a browser while students work. Don't miss the Clicker Questions, which can be readily downloaded for classroom use. Entire unit will take 2-3 weeks, but components may be pulled out separately. Can be used in a Physics First course, with teacher adaptation.

This is a computer lab created specifically for use with the PhET simulation "Wave on a String" (see Activities below). Students apply trigonometry and analyze how frequency, amplitude, and tension influence the motion of the wave. It may be downloaded as a Word file.

Here are two experiments on wave measurement in a ripple tank, appropriate for use in high school physical science or physics classrooms. Students are introduced to using the stroboscope to 'freeze' waves in a ripple tank, and to confirm the relationship between wave speed, frequency and wavelength.

Activities:

A wonderful way to introduce students to properties of waves. As the students open the applet, they are invited to "wiggle" a string to create a wave. They can set amplitude, frequency, damping, and string tension and watch the variable results. Waves can be manually or automatically generated. Finally, students can view the string's vibration with a fixed end, a loose end, or no end. See related teacher-created activity (directly below), developed for use in middle school classrooms with "Wave On a String".

Students explore relationships among frequency, amplitude, and wave speed in this inquiry-based activity developed to be used with the PhET simulation Wave on a String (see above). It is appropriate for 9th grade physical science or algebra-based introductory physics.

Try using this tutorial as a cooperative learning activity. Students explore the variables that affect wave speed by analyzing sample data and completing a question-and-answer set. It helps build understanding that wave speed is dependent on properties of the medium in which it moves, a central idea to be applied in problems relating to wave energy.

Superb inquiry-based problem to help students understand how spring tension, spring constant, and wave speed are related. The problem features a vibrating Slinky toy stretched to different lengths and given a "shake". Students must figure out how long it takes the wave pulse to travel the full length in both cases. They will discover for themselves that the time is the same. We suggest using this resource with the Physics Classroom tutorial above, "Speed of a Wave".

Content Support For Teachers:

This animated tutorial by Dan Russell illustrates the principle of wave superposition: when two (or more) waves travel through the same medium at the same time, the waves pass through each other without being disturbed. It's quite simple, but quite effective.

Assessment:

This is an excellent unit assessment with solutions, developed by a high school teacher to be used with the PhET simulation Wave on a String (see link under "Activities" above. It assesses understanding of fundamental wave properties, interference, standing waves, and beginning harmonics. It is formatted so that students can make responses online at the same time they are interacting with the simulation. Allow two class periods in computer lab.

Lesson Plans:

Students should whenever possible experiment for themselves using real equipment, rather than viewing only computer representations of ripple phenomena. This educators' guide gives detailed information about how to acquire, set up, and implement ripple tank experiments in the physical science or physics classroom. See related ripple tank activities developed by the same authors (below).

Ripple tanks provide a powerful way to help students visualize wave behavior in general. This set of 8 introductory labs allows students to become comfortable with ripple tanks by doing some simple experiments with pulses. Appropriate for grades 6-12, with supervision.

With the use of a ripple tank, students can observe the phenomenon of wave interference, which occurs when pulses and waves pass through each other. Many students are amazed to discover that the two waves continue on their way as if there had been no encounter. This set of four lab experiments demonstrates interference with two sources, using fingers and vibrators to create the disturbance. See Content Support below for links to background information on wave interference and superposition.

For physics teachers who want give their students a thought-provoking introduction to the quantum nature of light, have a look at this PhET Gold Star winning Power Point presentation. It was developed to supplement the PhET simulation Wave Interference (see link in Activities below). In this simulation, students view a virtual photon aimed through two slits to mimic the double-slit experiment. This supplementary resource helps students understand the concept of random behavior on the atomic scale. There are no calculations.

Activities:

This Java applet simulates wave oscillation by using the mouse to drive the motion of a vibrating string. Students can set amplitude, frequency, damping, and string tension and watch the results. Waves can be manually or automatically generated. Finally, students can view the string's vibration with a fixed end, a loose end, or no end.

Students interactively explore properties of waves as they view simulations of a dripping faucet, an audio speaker, and a laser. By observing wave sources and mediums for water, sound, and light, students can compare the behavior of different types of waves. Choose Light as a medium and add a second source or a pair of slits to create an interference pattern.

A set of three classroom demonstrations to be used with PhET simulations Wave on a String, Sound, and Wave Interference. Students explore wave reflection, patterns from interfering waves, and the Doppler Effect. The accompanying concept (clicker) questions may be downloaded in Power Point format and adapted for individual teacher use.

This simple applet illustrates the superposition principle as it applies to two waves interacting on a string. It would be a good choice for beginning physics students, as it contains no graphs and focuses only on pairs of waves interacting in one dimension. The applet automates the addition of the waves so that students can see why the Superposition Principle works.

Two high-quality video clips of wave motion in a ripple tank. One shows ripples from a stationary source, which can be analyzed to find frequency and wavelength. The second shows the source moving at constant velocity. May be viewed in step motion to allow for video analysis/measurement. For free software tools to do computer analysis of these videos frame-by-frame, see the "Tracker Video Analysis" item below.

This resource provides free software called "Tracker", developed to help students closely analyze the motion of objects in a short video clip. It also allows them to create dynamical models that overlay the video to see how well the model matches the real world. Detailed instructions are provided. And it's free.

A nice simulation for exploring the basics of wave reflection and refraction. It shows a single wavefront in slow motion as it reaches a medium with a different refractive index. Students can see how each point of the advancing wavefront is the center of a fresh disturbance and source of a new train of waves. They can adjust the refractive index and angle of incidence of either medium.

Content Support For Teachers:

A characteristic shared by all waves is that two or more of them moving simultaneously through the same space will superimpose and produce a combined effect. This tutorial, integrated with multiple interactive simulations, promotes understanding of wave superposition in a highly engaging format. Self-test is included.

When waves meet an obstacle or pass through small openings, they may appear to bend or spread out. This phenomena is called diffraction. We see examples of wave diffraction every day, but what is the physics behind it? This exemplary tutorial offers a multimedia tour of diffraction around objects, diffraction through slits, and various effects of diffraction.

Student Tutorials:

An introduction to wave behavior, created by a high school teacher. We suggest having students start with the section "Parts of a Wave", then proceed to the "Interference" section and watch the animations on constructive and destructive interference. These sections could be viewed using a classroom projector and one internet connection. For a related computer lab activity, see the "Wave Adder" in Activities above.

Assessment:

This is an excellent unit assessment with solutions, developed by a high school teacher to be used with the PhET simulation Wave on a String (see link under "Activities" above. It assesses understanding of fundamental wave properties, interference, standing waves, and beginning harmonics. It is formatted so that students can make responses online at the same time they are interacting with the simulation. **Allow two days if completed in computer lab.

Activities:

This applet simulates a harmonic coupled line of masses moving in one dimension. The load, damping, and stiffness of the springs are adjustable. It includes more complex concepts, such as phases and magnitudes of normal modes.

This model simulates the wave-generating machine created by John Shive at Bell Laboratories and made famous by the Similarities in Wave Behavior film. The simulation produces sinusoidal waves by twisting the first rod with a given frequency and amplitude. Students can set the end to be free or fixed, select a function for twisting the first rod, add a damping force, or change the length of the bars to visualize how a wave propagates in a non-uniform medium. Graphs are displayed that plot mechanical energy as a function of frequency. Advanced students can compute the speed of the traveling waves at various frequencies and plot dispersion curves.

References and Collections:

The phenomenon of resonance becomes very important in structural engineering, as can be observed in this historic video of the 1940 collapse of the Tacoma Narrows Bridge. The famous suspension bridge disaster occurred when high wind gusts set up a resonant vibration in the bridge, causing large-amplitude oscillatory motion. This video was digitally reformatted from the original film footage shot on the scene.

The science of music offers a great springboard to spark student interest in wave interference, standing wave patterns, and harmonics. This unique collection takes students on an exploration of the physics behind woodwinds, brass instruments, string, and more. Don't miss the "Sounds of World English" section: students can map their own speaking accents.

Student Tutorials:

This tutorial is presented as a conversation between a student and a teacher about wave resonance. It uses the context of waves bouncing around in a microwave and includes an interactive simulation. It also features an interesting analogy of laying bathroom tile to help students understand phase phenomena in wave resonance.

Standing waves are non-traveling vibrations. They are produced when an incident wave and the reflected wave interfere in a way that they appear to be standing still. Standing wave patterns are readily observable, notably in musical instruments. This exemplary interactive tutorial gives students a good foundation for understanding why and when this complex phenomenon occurs.

Lesson Plans:

A set of exemplary modules related to sound and music, developed for use in middle school and high school. It's broken into well-organized short components for teachers who may wish to teach only one element of this subject matter. Included are lessons and activities on frequency, wavelength, amplitude, pitch, the physics of sound, rhythms and beats, standing waves, harmonic series, and tuning systems. Worksheets include answer keys.

Activities:

This Java applet demonstrates waves on a vibrating string which is 'plucked' with the mouse. Options include adjusting the damping, force frequency (which can be set to resonance frequency), number of loads, simulation speed and tension. It is appropriate for use in AP physics or with students in a Part "B" high school course.

References and Collections:

Don't miss this collection of more than a dozen videos compiled by a physicist to help high school students understand the physics of sound. Observe a resonating glass break, view and observe jets breaking making a sonic boom, and more.

Don't be scared off by the title of this item. It is a fascinating resource that features a "thematic search engine" for locating information and examples of sound, sound waves, acoustics, hearing, and other related topics. Each topic is accompanied by audio clips from the library of the World Soundscape Project. For example, the topic "Hearing Loss" contains an audio simulation of normal and impaired hearing as a result of noise exposure. Students will enjoy playing around with this one.

The science of music offers a great springboard to spark student interest in wave interference, standing wave patterns, and harmonics. This unique collection takes students on an exploration of the physics behind woodwinds, brass instruments, string, and more. Don't miss the "Sounds of World English" section, which allows users to map their own speaking accents.

Content Support For Teachers:

This collection is a cost-free online textbook integrating the topics of waves, sound, music, and musical instruments. Designed for use in the high school classroom, it is quite comprehensive in scope. Teaching suggestions and tips are included.

Student Tutorials:

This page ventures into the real-world applications of wave properties associated with the physics of sound, including ultrasound, diffraction horns, noise cancellation, and harmonic synthesis. Especially engaging is the interactive wave applet that allows students to create their own sound waves, listen to predefined waveforms, or combine both.